An analogue of Ruzsa's conjecture for polynomials over finite fields

Jason P. Bell; Khoa D. Nguyen

An analogue of Ruzsa's conjecture for polynomials over finite fields

Number Theory 2019-10-21 v1

Authors: Jason P. Bell , Khoa D. Nguyen

Abstract

In 1971, Ruzsa conjectured that if $f:\ \mathbb{N}\rightarrow\mathbb{Z}$ with $f(n+k)\equiv f(n)$ mod $k$ for every $n,k\in\mathbb{N}$ and $f(n)=O(\theta^n)$ with $\theta<e$ then $f$ is a polynomial. In this paper, we investigate the analogous problem for the ring of polynomials over a finite field.

Keywords

ruzsa conjecture polynomials finite fields congruences growth condition

Cite

@article{arxiv.1910.08255,
  title  = {An analogue of Ruzsa's conjecture for polynomials over finite fields},
  author = {Jason P. Bell and Khoa D. Nguyen},
  journal= {arXiv preprint arXiv:1910.08255},
  year   = {2019}
}

Related papers

View all related →